Path Integral Formulation of Noncommutative Quantum Mechanics

TL;DR

This paper develops a phase-space path integral approach to noncommutative quantum mechanics, demonstrating its equivalence to the traditional operator method and applying it to compute the partition function of a noncommutative harmonic oscillator.

Contribution

It introduces a novel phase-space path integral formulation for noncommutative quantum mechanics and proves its equivalence to the operator formalism.

Findings

Path integral formulation is equivalent to operator formalism.

Partition function of noncommutative harmonic oscillator is explicitly calculated.

Provides a new computational tool for noncommutative quantum systems.

Abstract

We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic oscillator is calculated.